Sumsets in quadratic residues
Volume 164 / 2014
Acta Arithmetica 164 (2014), 221-243
MSC: 11B13, 11B50, 11B75.
DOI: 10.4064/aa164-3-2
Abstract
We describe all sets $A \subseteq {\mathbb F}_p$ which represent the quadratic residues $R \subseteq {\mathbb F}_p$ in the sense that $R=A+A$ or $R=A\mathbin {\hat{+} }A$. Also, we consider the case of an approximate equality $R \approx A+A$ and $R \approx A\mathbin {\hat{+}} A$ and prove that $A$ is then close to a perfect difference set.
